Find (a) E(X) (b) E (X²) (c) E [(X – 1)²]

Q: 2. . If f(x) dx = 4 and 3g(x) dx = -9, evaluate [² [3f(x) + g(x)] dx

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Q: 2. The discrete random variable X has the probability function kx, x = 2,4, 6 P(X = x) = - 2), x = 8…

A: From the given information, it is clear that,  The discrete random variable X has a probability…

Q: find a general formula for f (n)(x). f (x) = x−3/2

A: Given, f (x) = x−3/2 To evaluate, fn(x)

Q: (a) If we assume that the distribution of the temperature increases for the 29 men is symmetric and…

A: From given Date we have : mean x=2.31, standard deviation is s=0.96

Q: If E (X) = 1 and Var (X) = 4 then E (X² + 2X – 1) = :- 1)

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Q: Find f(x).

A: Given,

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A: The functions are given by fx = 2xgx = x+5 To evaluate: The expressions of f∘gx , g∘fx and the value…

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Q: Which is true for the f (x)= (2x-4x)e A. f(x)=e* B. f(x)=e*-1 C. f(x)=e D. f(x)=e

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Q: b) [F(x) then find f(x). If 3 In(x)/ sin(3x) − 3e³ + x² + 3. - f(x)dx= 3 ln([x]) + 3x + C

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Q: Find a formula for f(") (x) if f(x) = e-10: fln)(z) =[]

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Q: Show that E(X-µ)³ = E(x³) −3 [E (x²) ][E(X)] + 2[E(X)]³

A: The linearity of expectation property: With the assumption that, Xi's (i=1,2,...n) with n positive…

Q: For the function f(x,y)= (x² + y²) tan(ln(xy)) + e(x-y) which of the following is the value of…

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Q: Find a formula for f (z) if f(z) = I+1 f '(z) =O ( )'(2) =D-

A: We will use concept of inverse function and differentiation of a function.

Q: If h(x) = [f (x)]2 + 1g(x), determine h(1) and h(1), given that f (1) = 1, g(1) = 4, f (1) = -1,…

A: Given: hx=fx2+gx  ……1   Also, f1=1g1=4……2   and, f'1=-1g'1=4……3

Q: Find a formula for f−1(x) and then verify that f−1(f(x))=x and ff−1(x)=x.   ​f(x)=

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Q: (b) Find a formula for the inverse of the functiony= e2x-1,

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Q: x(n) = 3 [2n + 4″]

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Q: Given that E(X) = 3, and E(X²) = 10. Find E[(5X +3)²].

A: From the provided information, E (X) = 3 and E (X2) = 10

Q: Define the Null Hypothesis and give an example

A: In statistics null hypothesis say that there is no statistical significance. It generally states…

Q: Let E(X)=−7,E(Y)=4,var(X)=16 and var(Y)=8 Calculate (a) E(2X+4Y). (b) E(X − 2Y − 2022). (c) var(2X…

A: According our policy we can answer only first three subpart for remaining please repost the…

Q: Let f(x)=1/ x−2 and g(x)=(2/x)+2. Then (f∘g)(x)= (g∘f)(x)=

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Q: Find a general formula for f (n)(x). f (x) = x−1/2

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Q: | [10f(x) – g(x)]dx if Find 5 5 f(x)dx = 7 and g(x)dx = 6. %3D | [10f(x) – g(x)]dx = i

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Q: b. 8(x) = E ()" k = 1

A: domain: where function is defined

Q: Given f(x)=√x+1, g(x) = 3−*, h(x) = cosx, m(x) = log[-(x-4)] and p(x) = x-3 a. f(x) + g(x) b. g(x) -…

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Q: If f(x) = x√(x+3) and a=2, find (f-1)'(a). f is a one to one function

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Q: Given that f(x) = x? + læ and g(x) = x + 5, calculate. f(g(1)) = g(f(1)) =| %3D

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Q: - f«) = f(x) = E n=1

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Q: Find t(4)(n) for the function t(n)=3n-1/3 +2n5/3

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Q: Let X - x? (s). Find (a) E (1+2X + X²) where E (g (x)) = 6° g (x) fx (x) dx. (b) the characteristic…

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